In the 1930s, bulldozers clearing jungle for banana plantations in southern Costa Rica began turning up giant stone balls, some taller than a person and weighing as much as a loaded truck. Workers dynamited many of them looking for gold inside. Nearly a century later, nobody can say for certain how they were carved so precisely, or what they were for.

At eleven on a Sunday morning in 1978, something detonated over a small iron-mining island in Newfoundland. Fuse boxes threw blue flame across rooms, televisions burst, a shed came off its foundation with the chickens inside, and two neat holes were punched into a field. American satellites built to catch nuclear tests registered the flash, and Los Alamos sent scientists. Nearly fifty years later the file is still open.

More than a hundred hollow bronze dodecahedra have been dug up across the northern Roman provinces, each pierced by holes of different sizes. Not one Roman text, inscription or image mentions them. In 2023 a field in Lincolnshire produced the finest example yet, and the mystery only deepened.

On a Victorian bridge outside Dumbarton, dogs have been going over the same few metres of parapet for seventy years, almost always on clear days, almost always long-nosed breeds. In 2005 two specialists went looking at the bridge through a dog's eyes and came back with an answer involving a smell no human can detect. The answer still has holes in it.

For more than a hundred years, travellers crossing outback Queensland have described a light that rises out of the dark, hovers above the horizon, and follows them for kilometres. In 1992 a neuroscientist built one to order, using nothing but a car and ten kilometres of empty road. Boulia was not entirely grateful.

For generations the villagers of Shiyan Beicun believed their ponds were bottomless. In 1992 four of them bought pumps to find out, and drained the water off the roof of a hand-carved hall the size of a church. Twenty-four of them have now been opened, and not one line of Chinese history mentions that they exist.

Across the highlands of northern Laos stand thousands of carved stone jars, some weighing fourteen tonnes. A French archaeologist called them tombs in the 1930s. Then the bombs fell, and it took eighty years to get back to the question.

In July 1970 a US test missile carrying radioactive cobalt came down four hundred miles inside Mexico, and the American army built a railhead, a road and a camp to take it home. What stayed behind in the Chihuahuan Desert was a story about radios that will not work. Here is the documented record, and exactly where it runs out.

Ninety-two artificial islands sit in a lagoon off Pohnpei, walled with basalt logs that weigh up to fifty tonnes each. Dating puts the first courses at around 1180 CE. Nobody has yet explained how the stone crossed the island and floated onto the reef.

On a January afternoon in 1981 a farmer in southern France heard a whistle in his garden and saw something settle on the terrace below him. Within a day gendarmes were on their knees collecting soil. Within two years a French government space agency had published the most detailed physical-trace report it would ever release. Forty-five years later, nobody agrees on what made the mark.

A 250 hectare wood on the edge of Cluj-Napoca is routinely called the most haunted forest on Earth. Behind the label sit four photographic negatives from August 1968, a circular clearing where trees will not grow, and decades of measurements that were never published. Here is what can actually be documented, and what cannot.

In late 1977, people on a small island at the mouth of the Amazon began arriving at the clinic with burns, puncture marks and stories of beams of light coming through their roofs at night. The Brazilian Air Force sent an officer to find out what was happening. Twenty years later, he broke his silence, and then he was dead.